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Miha Kralj
2026-03-13 13:47:10 -07:00
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lib/trends_FIR/crma/Crma.md
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| **Signature** | [crma_signature](crma_signature.md) |
- CRMA fits a degree-3 polynomial $y = a_0 + a_1 x + a_2 x^2 + a_3 x^3$ to the most recent $N$ bars via ordinary least squares, then returns the fitt...
- Parameterized by `period`.
- Output range: Tracks input.
- Requires `period` bars of warmup before first valid output (IsHot = true).
- **Similar:** [SMA](../sma/Sma.md), [TrIMA](../trima/trima.md) | **Complementary:** Trend strength indicators | **Trading note:** Cubic-Root weighted MA; gentle weighting profile between uniform (SMA) and triangular (TrIMA).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
CRMA fits a degree-3 polynomial $y = a_0 + a_1 x + a_2 x^2 + a_3 x^3$ to the most recent $N$ bars via ordinary least squares, then returns the fitted endpoint value $a_0$. By capturing inflection and curvature that linear and quadratic models miss, CRMA tracks S-shaped reversals and accelerating trends with measurably lower endpoint error than LSMA or QRMA on non-stationary price series. The cost is a 4x4 linear system solve per bar, which is O(1) once power sums are accumulated in O(N).
@@ -132,4 +130,4 @@ O(N) per bar. For default N = 14: ~347 cycles. Resync re-computes sums every 100
| 4×4 Gaussian elimination | No | Fixed scalar 64-op system; not worth SIMD setup |
| Polynomial evaluation | No | 4-term Horner; scalar is fastest for degree 3 |
Batch throughput for the sum and cross-product phases: AVX2 achieves ~4× scalar. Gaussian elimination and Horner evaluation remain scalar. Net batch speedup for N = 14, large series: approximately 2.5× over fully scalar.
Batch throughput for the sum and cross-product phases: AVX2 achieves ~4× scalar. Gaussian elimination and Horner evaluation remain scalar. Net batch speedup for N = 14, large series: approximately 2.5× over fully scalar.